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Superpixels have become very popular in many computer vision applications. Nevertheless, they remain underexploited since the superpixel decomposition may produce irregular and non stable segmentation results due to the dependency to the…
Objects with symmetries are common in our daily life and in industrial contexts, but are often ignored in the recent literature on 6D pose estimation from images. In this paper, we study in an analytical way the link between the symmetries…
We introduce AlphaTablets, a novel and generic representation of 3D planes that features continuous 3D surface and precise boundary delineation. By representing 3D planes as rectangles with alpha channels, AlphaTablets combine the…
This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form $A(x)\dot{x} = F(x)$, $x\in\mathbb{R}^{2}$, where $F$ is a vector field and $A$ is a matrix valued function. Using techniques…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
Complex networks have been widely used in science and technology because of their ability to represent several systems. One of these systems is found in Biochemistry, in which the synthesis of new nanoparticles is a hot topic. However, the…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
Points of interest on a map such as restaurants, hotels, or subway stations, give rise to categorical point data: data that have a fixed location and one or more categorical attributes. Consequently, recent years have seen various set…
Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…
The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms…
This research is motivated by studying image processing algorithms through a topological lens. The images we focus on here are those that have been segmented by digital Jordan curves as a means of image compression. The algorithms of…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…